Asymptotic convergence of the extremes of a sequence of geometric type random variables

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Résumé

In this paper, we give some contributions to the analysis of the behavior of the extremes of a category of random variables (r.v.) of geometric type. First, we exhibit a subsequence making certain r.v. of integer part converge. Then we prove the convergence in law of extremes of a sequence of geometric type r.v. Finally, we prove the mean convergence of the extremes of a sequence of geometric type r.v.

Mots-clés

Subsequence, Sequence (biology), Convergence (economics), Type (biology), Convergence of random variables, Random variable, Weak convergence, Geometric series, Integer (computer science)